A metal sheet, in particular a thin steel sheet, is usually produced by rolling a material through rolling mill rolls. In this case, the sheet during rolling is elongated in the rolling direction while being rolled into a sheet with a reduced thickness.
Said elongation of the sheet during rolling in the rolling direction depends upon the draft (i.e., [thickness at the roll entry-- thickness at the roll exit]/thickness at the roll entry), and the distribution of said elongation in the width direction is determined by the thickness distribution in the width direction before rolling and the thickness distribution in the width direction after rolling. The above-mentioned thickness distribution in the width direction after rolling is influenced by deformation of rolling mill rolls such as (a) elastic deformation of the mill rolls, (b) thermal expansion of the mill rolls caused by the heat input from the sheet in rolling to the mill rolls, (c) wear of the mill rolls resulting from friction between the sheet during rolling and the mill rolls.
For such reasons, when the elongation of the sheet during rolling in the rolling direction is not uniform and there occur differences in said elongation in the width direction, compressive and tensile residual stresses are produced in the finished sheet in the rolling direction. More specifically, since a small thickness is obtained in the case of a large draft and a large thickness is obtained in the case of a small draft, compressive stresses remain in the part of the finished sheet with a small thickness and tensile stresses remain in the part of the finished sheet with a large thickness. When these residual stresses exceed a certain limit, the finished sheet undergoes deformation out of the original plane, resulting in a phenomenon called "buckling". This is generally called the defective flatness of finished sheet.